Bound the problem from two different directions.
First, start with your process capability. What tolerance can you actually hold? This will vary greatly depending on whether you are doing casting vs milling vs grinding etc. If you have a bunch of similar parts lying around, measure them and compute the standard deviation. Remember that 68% of parts will be within +/- 1 std dev, 95% within two, etc. E.g. if you have a mill that's producing parts with a standard deviation of say 0.010", then only a few per million would be outside of +/- 0.060". That sets your lower bound. Any less than this, and you'll be scrapping parts that you don't want to scrap. If you don't have any similar parts, then do some research on typical tolerances using your process, whatever it is, and probably round up a little.
Then, thing about what dimension you need the part to have to satisfy fit form and function. You said it doesn't have any engineering requirements, but it does have to have something. If the nominal dimension is 2", I'm sure the part wouldn't work if the shop gave you something that was 200". Figure out the biggest and smallest parts that would actually work. This sets the upper bound of your tolerance. E.g. maybe it's +/- 1".
So now you've got a range. in our example above, if your tolerances are any tighter than +/- 0.06", your shop can't make them and that will make it expensive. If it's looser than +/- 1.00", the parts won't work. Anywhere in between will be perfectly fine, so just pick something that range. Split the difference and call it +/- 0.5" and you're done.